Precalculus

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Precalculus

A 2-in-1 value: Thinkwell's Precalculus combines concepts from College Algebra with Trigonometry for a comprehensive experience of precalculus mathematics. Our Precalculus has hundreds of video tutorials and thousands of automatically graded exercises with step-by-step feedback, covering everything in the most popular textbooks, so you have all of the pre-calculus math help you need to prepare for Calculus.

Thinkwell's Precalculus video tutorials feature award-winning teacher Edward Burger, who has a unique ability to break down concepts and explain examples in ways that stick with students. Between having the best math teacher, 24/7 availability, and one fixed price instead of an hourly rate, Thinkwell Pre-Calculus is better than a tutor. It's the ultimate pre-calculus study aid.

Printable full-color illustrated notes help you review what you've learned in the video lesson

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Workbook, Notes, sample problems, exercises, and practice problems

Study without a computer. Our workbook companion contains the same lecture notes and sample problems that are delivered online, as well as some additional exercises, all in a convenient print format. Answers to the odd-numbered exercises are in the back of the book. Online Subscription is required; workbook not sold separately.

7.4.3 Solving Trigonometric Equations with Coefficients in the Argument

7.4.4 Solving Trigonometric Equations Using the Quadratic Formula

7.4.5 Solving Word Problems Involving Trigonometric Equations

7.5 The Sum and Difference Identities

7.5.1 Identities for Sums and Differences of Angles

7.5.2 Using Sum and Difference Identities

7.5.3 Using Sum and Difference Identities to Simplify an Expression

7.6 Double-Angle Identities

7.6.1 Confirming a Double-Angle Identity

7.6.2 Using Double-Angle Identities

7.6.3 Solving Word Problems Involving Multiple-Angle Identities

7.7 Other Advanced Identities

7.7.1 Using a Cofunction Identity

7.7.2 Using a Power-Reducing Identity

7.7.3 Using Half-Angle Identities to Solve a Trigonometric Equation

8. Applications of Trigonometry

8.1 The Law of Sines

8.1.1 The Law of Sines

8.1.2 Solving a Triangle Given Two Sides and One Angle

8.1.3 Solving a Triangle (SAS): Another Example

8.1.4 The Law of Sines: An Application

8.2 The Law of Cosines

8.2.1 The Law of Cosines

8.2.2 The Law of Cosines (SSS)

8.2.3 The Law of Cosines (SAS): An Application

8.2.4 Heron's Formula

8.3 Vector Basics

8.3.1 An Introduction to Vectors

8.3.2 Finding the Magnitude and Direction of a Vector

8.3.3 Vector Addition and Scalar Multiplication

8.4 Components of Vectors and Unit Vectors

8.4.1 Finding the Components of a Vector

8.4.2 Finding a Unit Vector

8.4.3 Solving Word Problems Involving Velocity or Forces

8.5 Complex Numbers in Trigonometric Form

8.5.1 Graphing a Complex Number and Finding Its Absolute Value

8.5.2 Expressing a Complex Number in Trigonometric or Polar Form

8.5.3 Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form

8.6 Powers and Roots of Complex Numbers

8.6.1 Using DeMoivre's Theorem to Raise a Complex Number to a Power

8.6.2 Roots of Complex Numbers

8.6.3 More Roots of Complex Numbers

8.6.4 Roots of Unity

8.7 Polar Coordinates

8.7.1 An Introduction to Polar Coordinates

8.7.2 Converting between Polar and Rectangular Coordinates

8.7.3 Converting between Polar and Rectangular Equations

8.7.4 Graphing Simple Polar Equations

8.7.5 Graphing Special Polar Equations

9. Systems of Equations and Matrices

9.1 Linear Systems of Equations

9.1.1 An Introduction to Linear Systems

9.1.2 Solving a System by Substitution

9.1.3 Solving a System by Elimination

9.2 Linear Systems of Equations in Three Variables

9.2.1 An Introduction to Linear Systems in Three Variables

9.2.2 Solving Linear Systems in Three Variables

9.2.3 Solving Inconsistent Systems

9.2.4 Solving Dependent Systems

9.2.5 Solving Systems with Two Equations

9.3 Applying Linear Systems

9.3.1 Investments

9.3.2 Solving with Partial Fractions

9.3.3 Partial Fractions: Another Example

9.4 Nonlinear Systems

9.4.1 Solving Nonlinear Systems Using Elimination

9.4.2 Solving Nonlinear Systems by Substitution

9.5 Matrices

9.5.1 An Introduction to Matrices

9.5.2 The Arithmetic of Matrices

9.5.3 Multiplying Matrices by a Scalar

9.5.4 Multiplying Matrices

9.6 Solving Systems Using the Gauss-Jordan Method

9.6.1 Using the Gauss-Jordan Method

9.6.2 Using Gauss-Jordan: Another Example

9.6.3 Using the Gauss-Jordan Method with Three Equations

9.6.4 Gaussian Elimination with Three Equations

9.7 Evaluating Determinants

9.7.1 Evaluating 2x2 Determinants

9.7.2 Evaluating nxn Determinants

9.7.3 Evaluating a Determinant Using Elementary Row Operations

9.7.4 Finding a Determinant using Expanding by Cofactors

9.7.5 Applying Determinants

9.8 Cramer's Rule

9.8.1 Using Cramer's Rule

9.8.2 Using Cramer's Rule in a 3x3 Matrix

9.9 Inverses and Matrices

9.9.1 An Introduction to Inverses

9.9.2 Inverses: 2x2 Matrices

9.9.3 Another Look at 2x2 Inverses

9.9.4 Inverses: 3x3 Matrices

9.9.5 Solving a System of Equations with Inverses

9.10 Working with Inequalities

9.10.1 An Introduction to Graphing Linear Inequalities

9.10.2 Graphing Linear and Nonlinear Inequalities

9.10.3 Graphing the Solution Set of a System of Inequalities

9.11 Linear Programming

9.11.1 Solving for Maxima-Minima

9.11.2 Applying Linear Programming

10. Special Topics

10.1 Conic Sections: Parabolas

10.1.1 An Introduction to Conic Sections

10.1.2 An Introduction to Parabolas

10.1.3 Determining Information about a Parabola from Its Equation

10.1.4 Writing an Equation for a Parabola

10.2 Conic Sections: Ellipses

10.2.1 An Introduction to Ellipses

10.2.2 Finding the Equation for an Ellipse

10.2.3 Applying Ellipses: Satellites

10.2.4 The Eccentricity of an Ellipse

10.3 Conic Sections: Hyperbolas

10.3.1 An Introduction to Hyperbolas

10.3.2 Finding the Equation for a Hyperbola

10.3.3 Applying Hyperbolas: Navigation

10.4 Conic Sections

10.4.1 Identifying a Conic

10.4.2 Name That Conic

10.4.3 Rotation of Axes

10.4.4 Rotating Conics

10.5 The Binomial Theorem

10.5.1 Using the Binomial Theorem

10.5.2 Binomial Coefficients

10.5.3 Finding a Term of a Binomial Expansion

10.6 Sequences

10.6.1 General and Specific Terms

10.6.2 Understanding Sequence Problems

10.6.3 Series Notation, Definitions and Evaluating

10.6.4 Solving Problems Involving Arithmetic Sequences

10.6.5 Finding the Sum of an Arithmetic Sequence

10.6.6 Solving Problems Involving Geometric Sequences

10.6.7 Finding the Sum of a Geometric Sequence

10.7 Induction

10.7.1 Proving Formulas Using Mathematical Induction

10.7.2 Examples of Induction

10.8 Combinations and Probability

10.8.1 Solving Problems Involving Permutations

10.8.2 Solving Problems Involving Combinations

10.8.3 Independent Events

10.8.4 Inclusive and Exclusive Events

About the Author

Edward Burger

Edward Burger is an award-winning professor with a passion for teaching mathematics.

Since 2013, Edward Burger has been President of Southwestern University, a top-ranked liberal arts college in Georgetown, Texas. Previously, he was Professor of Mathematics at Williams College. Dr. Burger earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.